Steven Lu (UQAM)
Title: Hyperkahler manifolds dominable by C^n
Abstract: Compact hyperkahler manifolds have been one of the principal focus of many aspects of recent activities in complex algebraic geometry, their singular analogs forming one principal and particular class of objects in the birational building blocks of algebraic varieties. In this talk, I will first review my dominability results with Greg Buzzard on K3 surfaces before delving into hyperkahler manifolds, which are higher dimensional analogs of K3s, joint with Ljudmila Kamenova. Related work joint also with Verbitsky and Bogomolov will also be mentioned as backdrop and motivation from the perspective of (anti)hyperbolicity, holomorphic analog of rational connectedness (and of unirationality at times) in the Ricci flat setting. Two principal series of examples, the Hilbert schemes of points on K3 (and
abelian) surfaces and the generalized Kummer varieties will be shown to be dominable, as well as Lagrangian fibred hyperkahler manifolds, either doubly so or satisfying the usual ansatz. We will elucidate further the geometry and their behaviour in moduli space as possible prelude to
generalizing these partial results time permitting.
Location: in person at UQAM PK-5675
or online at Zoom meeting 86352363947